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ConfidenceLevel

是 LinearModelFit 和其它拟合函数的选项，它指定生成不同置信及预测区间/带所使用的水平.

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ConfidenceLevel

ConfidenceLevel

是 LinearModelFit 和其它拟合函数的选项，它指定生成不同置信及预测区间/带所使用的水平.

更多信息

  • ConfidenceLevel 影响与置信区间相关的属性值.
  • 缺省设置是 95% 置信水平.
  • 该值应该是位于 0 和 1 之间的一个数值.
  • 对于某些类型的模型，FittedModel[…][prop,ConfidenceLevel->c] 可以用于提取指定置信水平的属性. »

范例

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基本范例  (1)

执行线性拟合并将默认置信水平设置为 99%：

Wolfram Language code: lm = LinearModelFit[{...}, x, x, ConfidenceLevel -> 0.99]

获取该置信水平的的平均预测带：

Wolfram Language code: lm["BestFitAround"]

范围  (3)

在拟合后设置置信水平：

Wolfram Language code: data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}};
Wolfram Language code: lm = LinearModelFit[data, x, x]

Estimates at the default 95% level:

Wolfram Language code: lm["ParameterEstimates"]//Query[All, {"BasisFunction", "ConfidenceInterval"}]

Estimates at the 90% level:

Wolfram Language code: lm["ParameterEstimates", ConfidenceLevel -> .9]//Query[All, {"BasisFunction", "ConfidenceInterval"}]

设置非线性模型的置信水平：

Wolfram Language code: data = Table[{x, 3 Sin[2x] + RandomReal[{-.2, .2}]}, {x, RandomReal[5, 10]}];
Wolfram Language code: nlm = NonlinearModelFit[data, a Sin[b x], {a, b}, x, ConfidenceLevel -> .9]
Wolfram Language code: nlm["ParameterConfidenceIntervalTable"]

用通常缺省的置信水平：

Wolfram Language code: nlm["ParameterConfidenceIntervalTable", ConfidenceLevel -> .95]

广义的线性模型：

Wolfram Language code: data = {{0, 1}, {1, 1.5}, {3, 2}, {5, 4}};
Wolfram Language code: glm = GeneralizedLinearModelFit[data, x, x, ExponentialFamily -> "InverseGaussian"]
Wolfram Language code: glm["ParameterConfidenceIntervalTable", ConfidenceLevel -> .99]

应用  (1)

某些数据的拟合：

Wolfram Language code: SeedRandom[1]; data = Table[{x, 1.2 Sin[2 x] + RandomReal[{-.2, .2}]}, {x, 10}]
Wolfram Language code: nlm = NonlinearModelFit[data, a Sin[b x], {a, b}, x]

获取多个置信水平下的置信区间以进行比较：

Wolfram Language code: intervals = Table[Thread@{p, Interval /@ nlm["ParameterConfidenceIntervals", ConfidenceLevel -> p]}, {p, {.8, .85, .9, .95, .99}}]

绘制置信区间与置信水平之间的关系：

Wolfram Language code: ListPlot[Transpose[intervals], PlotLegends -> {a, b}, PlotTheme -> "Detailed", FrameLabel -> {"ConfidenceLevel", "ConfidenceInterval"}]

属性和关系  (1)

ConfidenceLevel 影响所有 FittedModel 属性中的置信水平：

Wolfram Language code: lm = LinearModelFit[Range[5], x ^ 2, x]

用缺省的 95% 置信水平时的置信区间：

Wolfram Language code: Query[All, All, "ConfidenceInterval"]@lm[{"MeanPredictions", "SinglePredictions", "ParameterEstimates"}]

用 99% 置信水平的区间：

Wolfram Language code: Query[All, All, "ConfidenceInterval"]@lm[{"MeanPredictions", "SinglePredictions", "ParameterEstimates"}, ConfidenceLevel -> .99]
Wolfram Research (2008)，ConfidenceLevel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ConfidenceLevel.html.

文本

Wolfram Research (2008)，ConfidenceLevel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ConfidenceLevel.html.

CMS

Wolfram 语言. 2008. "ConfidenceLevel." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ConfidenceLevel.html.

APA

Wolfram 语言. (2008). ConfidenceLevel. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ConfidenceLevel.html 年

BibTeX

@misc{reference.wolfram_2026_confidencelevel, author="Wolfram Research", title="{ConfidenceLevel}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ConfidenceLevel.html}", note=[Accessed: 07-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_confidencelevel, organization={Wolfram Research}, title={ConfidenceLevel}, year={2008}, url={https://reference.wolfram.com/language/ref/ConfidenceLevel.html}, note=[Accessed: 07-September-2026]}